Clustering and information in correlation based financial networks

Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no edges where the vertices correspond to stocks. Then, one by one, we insert edges between the vertices according to the rank of their correlation strength, resulting in a network called asset graph. We study its properties, such as topologically different growth types, number and size of clusters and clustering coefficient. These properties, calculated from empirical data, are compared against those of a random graph. The growth of the graph can be classified according to the topological role of the newly inserted edge. We find that the type of growth which is responsible for creating cycles in the graph sets in much earlier for the empirical asset graph than for the random graph, and thus reflects the high degree of networking present in the market. We also find the number of clusters in the random graph to be one order of magnitude higher than for the asset graph. At a critical threshold, the random graph undergoes a radical change in topology related to percolation transition and forms a single giant cluster, a phenomenon which is not observed for the asset graph. Differences in mean clustering coefficient lead us to conclude that most information is contained roughly within 10% of the edges.Comment: 11 pages including 14 figures. Uses REVTeX4. To be published in a special volume of EPJ on network

Dynamics of polymer ejection from capsid

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which a viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the escape times scale with polymer length, $\tau \sim N^\alpha$. We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) $\rho$ inside the capsid. For very low densities $\rho \le 0.002$ the polymer is only weakly confined by the capsid, and we measure $\alpha = 1.33$, which is close to $\alpha = 1.4$ obtained for polymer translocation. At intermediate densities the scaling exponents $\alpha = 1.25$ and $1.21$ for $\rho = 0.01$ and $0.02$, respectively. These scalings are in accord with a crude derivation for the lower limit $\alpha = 1.2$. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, $\rho \gtrapprox 0.25$. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.Comment: 10 pages, 6 figure

Critical evaluation of the computational methods used in the forced polymer translocation

In forced polymer translocation, the average translocation time, $\tau$, scales with respect to pore force, $f$, and polymer length, $N$, as $\tau \sim f^{-1} N^{\beta}$. We demonstrate that an artifact in Metropolis Monte Carlo method resulting in breakage of the force scaling with large $f$ may be responsible for some of the controversies between different computationally obtained results and also between computational and experimental results. Using Langevin dynamics simulations we show that the scaling exponent $\beta \le 1 + \nu$ is not universal, but depends on $f$. Moreover, we show that forced translocation can be described by a relatively simple force balance argument and $\beta$ to arise solely from the initial polymer configuration

Dynamic asset trees and Black Monday

The minimum spanning tree, based on the concept of ultrametricity, is constructed from the correlation matrix of stock returns. The dynamics of this asset tree can be characterised by its normalised length and the mean occupation layer, as measured from an appropriately chosen centre called the `central node'. We show how the tree length shrinks during a stock market crisis, Black Monday in this case, and how a strong reconfiguration takes place, resulting in topological shrinking of the tree.Comment: 6 pages, 3 eps figues. Elsevier style. Will appear in Physica A as part of the Bali conference proceedings, in pres

The role of the electrocardiographic phenotype in risk stratification for sudden cardiac death in childhood hypertrophic cardiomyopathy.

Aims The 12-lead electrocardiogram (ECG) is routinely performed in children with hypertrophic cardiomyopathy (HCM). An ECG risk score has been suggested as a useful tool for risk stratification, but this has not been independently validated. This aim of this study was to describe the ECG phenotype of childhood HCM in a large, international, multi-centre cohort and investigate its role in risk prediction for arrhythmic events. Methods and results Data from 356 childhood HCM patients with a mean age of 10.1 years (±4.5) were collected from a retrospective, multi-centre international cohort. Three hundred and forty-seven (97.5%) patients had ECG abnormalities at baseline, most commonly repolarization abnormalities (n = 277, 77.8%); left ventricular hypertrophy (n = 240, 67.7%); abnormal QRS axis (n = 126, 35.4%); or QT prolongation (n = 131, 36.8%). Over a median follow-up of 3.9 years (interquartile range 2.0–7.7), 25 (7%) had an arrhythmic event, with an overall annual event rate of 1.38 (95% CI 0.93–2.04). No ECG variables were associated with 5-year arrhythmic event on univariable or multivariable analysis. The ECG risk score threshold of >5 had modest discriminatory ability [C-index 0.60 (95% CI 0.484–0.715)], with corresponding negative and positive predictive values of 96.7% and 6.7% Conclusion In a large, international, multi-centre cohort of childhood HCM, ECG abnormalities were common and varied. No ECG characteristic, either in isolation or combined in the previously described ECG risk score, was associated with 5-year sudden cardiac death risk. This suggests that the role of baseline ECG phenotype in improving risk stratification in childhood HCM is limited.post-print967 K